Unitary Synthesis, the decomposition of a unitary matrix into a sequence of quantum gates, is a fundamental challenge in quantum compilation. Prevailing reinforcement learning (RL) approaches are often hampered by sparse reward signals, which necessitate complex reward shaping or long training times, and typically converge to a single policy, lacking solution diversity. In this work, we propose QFlowNet, a novel framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers. Our approach addresses two key challenges. First, the GFlowNet framework is fundamentally designed to learn a diverse policy that samples solutions proportional to their reward, overcoming the singlesolution limitation of RL while offering faster inference than other generative models like diffusion. Second, the Transformers act as a powerful encoder, capturing the non-local structure of unitary matrices and compressing a high-dimensional state into a dense latent representation for the policy network. Our agent achieves an overall success rate of 99.7% on a 3-qubit benchmark (lengths 1-12) and discovers a diverse set of compact circuits, establishing QFlowNet as an efficient and diverse paradigm for unitary synthesis.
Unitary Synthesis, the decomposition of a unitary matrix into a sequence of quantum gates, is a fundamental challenge in quantum compilation. Prevailing reinforcement learning (RL) approaches are often hampered by sparse reward signals, which necessitate complex reward shaping or long training times, and typically converge to a single policy, lacking solution diversity. In this work, we propose QFlowNet, a novel framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers. Our approach addresses two key challenges. First, the GFlowNet framework is fundamentally designed to learn a diverse policy that samples solutions proportional to their reward, overcoming the singlesolution limitation of RL while offering faster inference than other generative models like diffusion. Second, the Transformers act as a powerful encoder, capturing the non-local structure of unitary matrices and compressing a high-dimensional state into a dense latent representation for the policy network. Our agent achieves an overall success rate of 99.7% on a 3-qubit benchmark (lengths 1-12) and discovers a diverse set of compact circuits, establishing QFlowNet as an efficient and diverse paradigm for unitary synthesis.
Unitary Synthesis, the decomposition of a unitary matrix into a sequence of quantum gates, is a fundamental challenge in quantum compilation. Prevailing reinforcement learning (RL) approaches are often hampered by sparse reward signals, which necessitate complex reward shaping or long training times, and typically converge to a single policy, lacking solution diversity. In this work, we propose QFlowNet, a novel framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers. Our approach addresses two key challenges. First, the GFlowNet framework is fundamentally designed to learn a diverse policy that samples solutions proportional to their reward, overcoming the single-solution limitation of RL while offering faster inference than other generative models like diffusion. Second, the Transformers act as a powerful encoder, capturing the non-local structure of unitary matrices and compressing a high-dimensional state into a dense latent representation for the policy network. Our agent achieves an overall success rate of 99.7% on a 3-qubit benchmark(lengths 1-12) and discovers a diverse set of compact circuits, establishing QFlowNet as an efficient and diverse paradigm for unitary synthesis.
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the underlying combinatorial search space. Existing approaches suffer from misaligned optimization objectives, substantial training costs and limited generalization across different qubit counts. We mitigate these limitations by using supervised learning to approximate the minimum description length of residual unitaries and combining this estimate with stochastic beam search to identify near optimal gate sequences. Our method relies on a lightweight model with zero-shot generalization, substantially reducing training overhead compared to prior baselines. Across multiple benchmarks, we achieve faster wall-clock synthesis times while exceeding state-of-the-art methods in terms of success rate for complex circuits.
A reinforcement learning (RL) framework is introduced for the efficient synthesis of quantum circuits that generate specified target quantum states from a fixed initial state, addressing a central challenge in both the Noisy Intermediate-Scale Quantum (NISQ) era and future fault-tolerant quantum computing. The approach utilizes tabular Q-learning, based on action sequences, within a discretized quantum state space, to effectively manage the exponential growth of the space dimension. The framework introduces a hybrid reward mechanism, combining a static, domain-informed reward that guides the agent toward the target state with customizable dynamic penalties that discourage inefficient circuit structures such as gate congestion and redundant state revisits. This is a circuit-aware reward, in contrast to the current trend of works on this topic, which are primarily fidelity-based. By leveraging sparse matrix representations and state-space discretization, the method enables practical navigation of high-dimensional environments while minimizing computational overhead. Benchmarking on graph-state preparation tasks for up to seven qubits, we demonstrate that the algorithm consistently discovers minimal-depth circuits with optimized gate counts. Moreover, extending the framework to a universal gate set still yields low depth circuits, highlighting the algorithm’s robustness and adaptability. The results confirm that this RL-driven approach, with our completely circuit-aware method, efficiently explores the complex quantum state space and synthesizes near-optimal quantum circuits, providing a resource-efficient foundation for quantum circuit optimization.
One of the most important initial steps in quantum computing is high-fidelity quantum state preparation, because errors in it can affect the final computational result. Therefore, one of the major challenges is to design a quantum circuit that can achieve the desired target state accurately with a smaller number of gates. Traditionally, circuits are designed using predefined rules and mathematical decompositions, but this makes it difficult to design circuits for different and complex target states. This paper presents TATVA, a reinforcement learning (RL) system for synthesizing quantum circuits. TATVA views circuit synthesis as a sequential decision problem in which the agents select one gate at a time and calculate the fidelity after each applied gate, with the gate producing the highest fidelity selected for the circuit. The system introduces a parallel architecture that uses two RL agents, Deep Q-Network (DQN) and Proximal Policy Optimization (PPO), along with Qiskit's statevector simulator. The system can synthesize up to 5 qubits while achieving a fidelity of 0.999999 and producing compact circuits. After achieving the desired fidelity, it performs a post-hoc optimization step that reduces the circuit depth while preserving the achieved fidelity. The circuit is finalized using fidelity, success rate, gate count, and circuit depth. Target states that are not used during training are used to test whether the system has learned effectively and can generalize beyond the training states. This approach aims to enable automatic quantum circuit synthesis with high fidelity using reinforcement learning.
State preparation is currently the only means to provide input data for quantum algorithm, but finding the shortest possible sequence of gates to prepare a given state is not trivial. We approach this problem using reinforcement learning (RL), first on an agent that is trained to only prepare a single fixed quantum state. Despite the overhead of training a whole network to just produce one single data point, gradient-based backpropagation appears competitive to genetic algorithms in this scenario and single state preparation thus seems a worthwhile task. In a second case we then train a single network to prepare arbitrary quantum states to some degree of success, despite a complete lack of structure in the training data set. In both cases we find that training is severely improved by using QR decomposition to automatically map the agents' outputs to unitary operators to solve the problem of sparse rewards that usually makes this task challenging.
High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.